The cyclotron radius rc of an ion with the mass m, the elementary charge e, the charge number z, and the kinetic energy Ekin in a magnetic field of the flux density B is given by the following equation:
                              r          c                =                                            2              ⁢                              mE                kin                                              zeB                                    (        1        )            In the thermal energy range, e.g. at a temperature of 298 K, and in a magnetic field with the flux density of 7 Tesla, the cyclotron radius of a singly charged ion with mass 1,000 dalton is approximately a tenth of a millimeter. Normally, the ICR cell contains a large number of ions, and their masses can be quite different. Before detection, the cyclotron motion of the ions is excited by an oscillating (RF) electric field with a scanned frequency (“Chirp”). When the frequency of the scanned oscillating field becomes equal to the cyclotron frequency
                              v          c                =                  zeB                      2            ⁢            π            ⁢                                                  ⁢            m                                              (        2        )            of an ion with mass m and charge number z, its cyclotron motion gets resonantly excited. In this equation e is the elementary charge. Depending on the duration and the amplitude of the irradiated field, ions become accelerated and move to larger (excited) cyclotron orbits. This resonant excitation also forces ions with the same charge number-related mass (m/z), which initially circle randomly on small cyclotron orbits having completely different phases, to a completely coherent motion. At the end of the excitation process ions with the same charge number-related mass (m/z) form a cloud in which all ions move in phase. Coherently moving ions in this excited cloud induce image charges of the same magnitude at the detection electrodes that oscillate with the same frequency and with the same phase. Such oscillating image charges (image currents) generated by all excited ion clouds are recorded, amplified, and after Fourier transformation displayed as a frequency spectrum or, when a frequency to mass mapping exists, as a mass spectrum.
The magnetic field can trap ions in the plane perpendicular to the magnetic field lines so that they cannot radially escape the cell. To prevent the ions from escaping in the axial direction, an electric trapping field is required. Therefore, axially, at both ends of the cell, end electrodes (or end plates) are placed to which a relatively low DC voltage is applied, for example normally 1-2 volts. The polarity of this DC voltage is the same as that of the ions to be trapped. The mantle electrodes of a simple conventional cylindrical ICR cell are grounded, thus, an electric trapping field is formed in the cell between the end electrodes and the cylinder mantle. Ions with the mass m and the charge number z oscillate axially in the cell of the length a between the two end electrodes with a trapping frequency vT if a trapping voltage VT is applied:
                              v          T                =                              1                          2              ⁢              π                                ⁢                                                                      2                  ⁢                  α                  ⁢                                                                          ⁢                                      zeV                    T                                                                    ma                  2                                                      .                                              (        3        )            Here e is the elementary charge, and α a constant depending on the cell geometry. With this additional oscillation the ion performs a combination of three independent periodic motions in the cell: cyclotron and magnetron motions in the radial plane, and the trapping oscillations in the axial direction.
Although the applied electric trapping field helps keeping the ions from escaping the cell, it deteriorates the conditions for a clean measurement of the cyclotron frequency. Due to the radial components of the trapping field, the ions do not only circle on their pure cyclotron orbits. As a superimposed motion they follow epicycloidal magnetron orbits and they additionally oscillate in the axial direction with the trapping frequency. The magnetron motion is relatively slow compared to the cyclotron motion. Its frequency only depends on the magnetic field and the electric field. The size (or diameter) of the initial magnetron orbits of ions in the cell right after they are captured depends on how the ions are transferred to the cell: transferred by an electrostatic ion transfer optics or by an RF-multipole transfer optics, or whether or not they are captured using an electric field pulse orthogonal to their path and to the magnetic field (“sidekick”), etc. The initial magnetron radii are normally small, but they can be increased by asymmetric magnetic or electric fields that may excite the magnetron motion. A resistive detection circuit can also induce an increase in magnetron radii due to loss of the potential energy by image current damping.
In the presence of a trapping field, the frequency measured at the detection electrodes of the cell is no longer the unperturbed cyclotron frequency vc but the reduced cyclotron frequency vR:
                                          v            R                    =                                                    v                c                            2                        +                                                                                v                    c                    2                                    4                                -                                                      v                    T                    2                                    2                                                                    ,                            (        4        )            which is smaller by a magnetron frequency vM than the unperturbed cyclotron frequency:vR=vc−vM.  (5)The magnetron frequency of an ion of cyclotron frequency vc and a trapping frequency vT is:
                              v          M                =                                            v              c                        2                    -                                                                                          v                    c                    2                                    4                                -                                                      v                    T                    2                                    2                                                      .                                              (        6        )            
FIG. 1 shows the combined motion of an ion in an ICR cell in the magnetic field of the flux density B 1. The combination of the cyclotron motion 2, the trapping oscillation 3, of which the sinusoidal curve is shown in dashed lines 4, and the magnetron motion 5 produces the complicated resulting motion 6 of the ion around the electric field axis 7.
When an ion is axially introduced exactly in the middle of the ICR cell, it should normally not experience any electric field component perpendicular to its path. The radial components of the electric trapping field are distributed symmetrically around the axis of the DC electric field, i.e., normally around the axis of the cell. Thus, there is no perpendicular electric field component at the cell axis. However, if the electric field axis is displaced and does not coincide with the axis of the cell, then a perpendicular electric field component does exist at the cell axis. An ion that is introduced on axis into the cell experiences this field component, and the influence of the E×B fields immediately diverts it from its initial path. The same would happen if the ion were not introduced on axis, regardless of the presence of a field asymmetry. The ion now drifts perpendicular to both the magnetic field and that radial electric field component into the third dimension and starts an epicycloidal orbit that winds on a circle around the offset electric field axis. This is a magnetron orbit with an offset axis in reference to the cell axis. The magnetron radius is basically equal to the displacement of the electric field axis.
FIG. 2a is a partial drawing of a trapping plate 21 of an ICR cell with the ion introduction hole 20. The electric field axis 23 does not coincide here with the geometric axis 30 of the cell, and the radial electric field components 22 make the ion start moving on an epicycloidal 25 magnetron orbit around the electric field axis 23. The virtual magnetron circle 26 is shown in dashed lines. The magnetron radius is here equal to the displacement 27 of the electric field. Numeral 24 indicates the direction of the magnetic field lines being aligned perpendicular to the plane of illustration.
FIG. 2b shows an electric field axis 23a that is displaced by a much smaller amount 27a than in FIG. 2a. In this case, the ion entering the cell on axis is also influenced by the radial field components 22a and moves on a smaller magnetron orbit 25a around the displaced field axis. The virtual magnetron circle is here also shown in dashed lines 26a and has the same magnitude as the displacement 27a of the electric field. It is to be noted that the displacement of the field axis as well as the complete magnetron orbit 25a remains here within the limits of the ion introduction hole 20 of the ICR cell.
In a trapping field which is asymmetric and not concentric with the cell, severely shifted magnetron orbits can be formed, on which ions can come close to the mantle electrodes. During a cyclotron excitation on such a shifted magnetron orbit, ions can hit the cell walls and be lost before they are detected.
An asymmetry of the electric field inside the FT-ICR cell can be a consequence of many different effects. Some of them are discussed in the following.
FIG. 10a shows a classical cylindrical ICR cell with four mantle electrodes. Two of the opposite-sided mantle electrodes are used for the excitation of the ion cyclotron motion by applying an oscillating electric field and the other two mantle electrodes are used for the image current detection of the cyclotron frequency of the excited ion clouds. In conventional ICR cells the excitation and detection electrodes are of equal size (90° segments). In FIG. 10a the detection electrodes are numbered as 210, 212, but only one of the excitation electrodes 211 is visible in the figure. One of the trapping electrodes 205 is at the front end with the ion entrance hole 20 and the other one 206 at the back end of the cell.
A deviation of individual electrode shapes from the calculated ideal shapes or a deviation of the assembled cell from its ideal shape can cause asymmetry of the electric field inside the cell. Most of the conventional cylindrical cells have only four cell mantle electrodes which are cylindrically bent rectangular electrodes, and their end electrodes are flat circle shaped parts (confer 205, 206 in FIG. 10a). Although these shapes are mostly straightforward, deviations from perfect shapes can still occur if the tolerances are not correctly defined, if the individual electrodes are not cut out of one and the same cylindrical raw material, or if the assembly of the cell is not perfect. In the FT-ICR cells of more complex nature this remains a challenge. Cylindrical cells specially made for high resolution acquisitions contain, for example, more than one detection electrode pair for detection of multiples of the cyclotron frequency. Some of them can have sixteen cylinder mantle electrodes which need to be manufactured and assembled within narrow tolerances. There is a non-zero probability that some individual electrodes of a multitude of mantle electrodes of an ICR cell may deviate to a different extent from the corresponding ideal shape and/or alignment so that the ensuing perturbation of the desired ideal electric field axis may also be non-uniform, for instance, in that a radial shift of the electric field center varies along the longitudinal extension of the cell.
Manufacturing tolerances of parts, as well as deviations from precise assembly in case of compensated cylindrical FT-ICR cells which usually contain 28 or 36 cylinder mantle electrodes (7-section and 9-section cells are known in the art) can influence the electric field symmetry throughout the cell.
Dynamically harmonized cells do have a specially shaped cylinder mantle which usually contains twenty or more cylinder mantle electrodes. If the tolerances of the electrodes are not correctly kept, or if the final assembly of so many electrodes is not perfectly performed these cells are also susceptible to generate electric field errors inside. In a simplest case, these field errors can lead to a parallel displacement of the electric field axis from the geometric axis of the cell (uniform perturbation). In more complicated cases, however, these field errors may also lead to at least one of a tilting (e.g., the electric field axis and geometric axis of the ICR cell are not parallel any more), a bending (e.g., the electric field axis is not a straight line any more, but a non-linear 2D or 3D curve), and a rippling (e.g., the electric axis comprises a stepped pattern with abrupt shifts where a perturbation changes significantly) of the electric field axis (e.g., non-uniform perturbation).
FIG. 3a shows an example for a dynamically harmonized ICR cell 50, known from the patent application WO 2011/045144 A1 (E. Nikolaev et al.). This cell has leaf-shaped (e.g., 58) and inverse-leaf shaped (e.g., 55, 57, 59, 61) cylinder mantle electrodes. In FIG. 3a, the letter X denotes the cell axis. In order to divide the cell mantle into four equal 90°-individual electrode groups, four of the eight leaf electrodes are longitudinally divided into two halves (e.g., 56a, 56b). Thus the cell has four integral leaf electrodes, four split leaf electrodes or half-leaf electrodes, and eight inverse-leaf electrodes.
FIG. 3b displays the cylinder mantle electrodes open and unwound. There are two excitation groups E including five electrodes (60b, 61, 62, 63, 64a) and (69b, 70, 71, 72, 56a), respectively. Furthermore, there are two detection groups including five electrodes (56b, 57, 58, 59, 60a) and (65b, 66, 67, 68, 69a), respectively. In the detection groups often only the leaf and half-leaf electrodes (e.g., 56b, 58, 60a) and (e.g., 65b, 67, 69b) are used. The inverse-leaf electrodes (e.g., 57, 59, 66, 68) are normally not used as detection electrodes since these are connected to DC voltage power supplies and thus lead to noisy ICR signals. However, if the DC voltages are generated by a battery, the noise can be avoided, and all five electrodes in a detection group can be used for signal detection. All inverse-leaf plates may be supplied with a common variable DC voltage which normally does not differ too much from the trapping voltage of the end electrodes (e.g., 80, 81) of the cell.
Another cause of symmetry errors of the electric field inside the ICR cell may originate from the contact potentials of connectors from the power supply. The contact potentials can change the effective potentials appearing on the individual electrodes, and they can be slightly different from the voltages applied by the user at the instrument console. Depending on the location of these contact potential effects this problem can cause asymmetric electric field inside the cell.
Asymmetric electric fields in the ICR cell can also be a consequence of charging up of individual electrodes. Charging is a general process, which can appear due to various reasons. One of the reasons for electrode charging can be a high resistive connection of this electrode to the ground. Normally, after every acquisition cycle, the detection electrodes in the cell should be at ground potential. However, if they are connected to the ground over a large resistor, which picks up the extremely low induced image charge signal, this can make it difficult to have a quick and easy discharge after every acquisition cycle. The electrode may maintain its charged state for a while, even after the next acquisition cycle starts. In this way, an asymmetric electric field is induced in the cell due to an imperfectly discharged electrode. Needless to say that this type of charging may manifest itself at different individual mantle electrodes with different magnitudes whereby a non-uniform electric field perturbation along the cell axis may emerge.
A different type of electrode charging is surface charging. This usually happens if the metallic surface of the electrode carries a dielectric layer, which (a) can be polarized or charged and (b) cannot easily be discharged due to its lack of conductance. These non-conductive layers usually appear on electrodes due to chemical contamination of the vacuum system. It is known in mass spectrometry that in contaminated vacuum systems or in the presence of outgassing vacuum components, nonconductive layers can be deposited on surfaces of electrodes. This way, the actual voltage at the surface of this electrode can differ from the applied voltage. Applied voltages in the range of 1-2 volts can easily be varied due to surface charging by an amount of 20 to 100 mV, although in selected cases larger values can be observed. Experience shows that such dielectric layers can be dynamic. Depending on their chemical composition they can grow or they can get thinner. Their consistency can even change with time, heat and/or applied chemical “stress” (additional compounds introduced into the vacuum). As a consequence, the ratio of the applied voltage to the actual voltage of the electrode may change with time.
Contaminations of surfaces can also be caused by ions in the cell, but they can also originate from other sources in the vacuum system, external to the ICR cell. Trapped ions can be the source of the contamination within an ICR cell. In the long term, repeated ion ejections can lead to deposition of substances on the inside surface of the mantle electrodes which form a dielectric layer. An uneven distribution of surface contamination on individual longitudinal electrodes can lead to asymmetric surface charging. As a consequence, a radial displacement of the electric field center can have different magnitudes at different points along the cell axis, which in turn leads to a non-uniform electric field perturbation within the cell. Quenching prior to each acquisition cycle cleans the cell from remaining ions for the next acquisition. During a quench pulse a DC voltage of 20-30 volts of a polarity opposite to that of the trapped ions is applied to one of the trapping electrodes, and as a consequence all remaining ions in the cell are attracted to and hit this electrode. Depending on the compounds being measured, the quench event can also produce a dielectric layer on the inside of this trapping plate, which can then, due to surface charging, deteriorate the axial symmetry of the electric field. It depends on the chemical composition of the contaminant layer whether or not a strong bake-out at e.g., 300° C. eliminates it or if it even strengthens the insulation properties of the layer. Bake-out temperatures are often kept lower (around 150° C.) due to material-related reasons. Thus, the layers may not get completely eliminated. Layers of some specific compositions tend to polymerize at higher temperatures and can sometimes only be removed by mechanic scrubbing.
Contamination sources external to the ICR cell include the vacuum components that, for some reason, cannot be kept clean enough. In many cases external heating jackets used for bake-outs first increase the temperature of the walls of the vacuum chamber. The ICR cell is initially cold, and it gets warmer with some delay depending on the heat transfer coefficients of various components used in vacuum. Due to this delay, contaminants can initially thermally desorb off the vacuum chamber walls, can condense at the electrode surfaces of the cold ICR cell and cause surface charging.
One intrinsic property of the (fast) Fourier transform detection method is the appearance of harmonic frequencies of the measured (fundamental) mass peaks in a spectrum. In the ideal case of a perfectly symmetric electric field, and if the ions are injected in the middle into the ICR cell, only odd-numbered harmonic frequencies should appear in the spectrum due to a pure cyclotron motion around the center of the ICR cell. The intensities and distribution of the odd-numbered harmonics depend on the ion cyclotron radius and the arrangement of the detection electrodes. Any distortion/asymmetry of the electric field or improper injection of an ion packet into the ICR cell, however, entails a magnetron motion of the ions in the ICR cell. In such case, additional even-numbered harmonic frequencies of the main or fundamental ion signal appear in the spectrum.
In the following some fundamental rules about the appearance of the harmonics and the satellite peaks thereof are presented. The intensity of the second harmonic peak with the frequency of 2vR can be, for example, related to the position of the magnetron motion (vR being the reduced cyclotron frequency). If an ion is on the ICR cell axis prior to cyclotron excitation, the second harmonic peak no longer exists. Also, if the magnetron circle is concentric with the cell axis, the second harmonic does not exist either. Usually the ion detection time is long enough and takes several magnetron periods. Therefore, the averaging effect annihilates the second harmonic peak. As a general rule, if the center of the magnetron orbit approaches the cell axis, the intensity of the second harmonics becomes smaller. If the magnetron axis coincides with the cell axis, the second harmonics peak disappears, as simulations also show. It is always desirable that the axis of the magnetron orbit be as close as possible to the axis of the ICR cell. It should be coaxial with the cell axis, if possible.
The intensity of the second harmonic peak group, especially of the one peak with the frequency 2vR+vM (vM being the magnetron frequency), is related to the position of the corresponding ion in the cell prior to cyclotron excitation. Thus, it is related to both the position and the size of the magnetron orbit. If the magnetron diameter is large, this satellite peak is abundant and it oscillates and goes through two maxima and two minima during one single magnetron period. The maxima are generated by the ions that are on magnetron orbits at offset positions, specifically in sections with detection electrodes prior to their cyclotron excitation. The minima are generated by the ions that are on magnetron orbits at offset positions, specifically in sections with excitation electrodes, prior to their cyclotron excitation. During one complete cycle of the magnetron orbit, the 2vR+vM peak shows two maxima and two minima. The time between the capture of the ion in the FT-ICR cell and the excitation event defines this phase on the magnetron orbit. In the FT-ICR experiment, the time between the ion capture and the ion excitation can be varied and the ion can be cyclotron-excited at different points of the magnetron orbit. The (relative) abundance of the major satellite peak of the second harmonics can be plotted against this “post capture delay” (PCD) time for displaying the oscillating behavior of this peak. In the following, we will call such a plot a “post capture delay curve” or “PCD curve”.
A large and offset magnetron orbit limits the cyclotron excitation process of the ions and impairs the detected signal, leads to an increase of the intensity of the peaks associated with the even-numbered, e.g., second, harmonics in the Fourier transformed spectrum and to more abundant sidebands of the ion signal. In extreme cases, ions can be lost during the cyclotron excitation, when they are on large and offset magnetron orbits that are close to the cylinder mantle electrodes.
Additionally, a large magnetron orbit can cause problems when using a multiple frequency detection method. Multiple frequency detection multiplies the resolving power of the detected mass peaks. In an ICR cell multiple frequency signals can be obtained if more than two detection electrodes (e.g., four, eight, etc.) are used. However, this method can only be successfully applied if ions have no magnetron orbits or if these are vanishingly small. Moderate or large magnetron orbits severely complicate the ICR mass spectra and reduce the signal intensity of the multiple-frequency mass peaks.
The invention described in the patent application of G. Baykut, J. Friedrich, R. Jertz, and C. Kriete, (U.S. Ser. No. 13/767,595 filed on Feb. 14, 2013, the priority of which is herewith claimed for its entire disclosure) can be used for correction of asymmetric electric fields in an ICR cell that lead to offset magnetron orbits. It helps identifying a displacement of the electric field axis and trimming the displaced magnetron axis back to the cell axis. Another submitted but not yet published European patent application of R. Jertz and G. Baykut (application number 13004771.5, filed on Oct. 11, 2013) describes a different approach for a further reduction of the size of the initial magnetron orbit.
If the magnetron orbit of an ion has any radial offset from the ICR cell axis, the intensity oscillation of the peak with the frequency of 2vR+vM shows differently abundant maxima and minima during one single magnetron period. Thus, the PCD curve shows two maxima and two minima which are not of equal intensity. If the radial offset is in direction of one of the excitation electrodes the PCD curve has one deep and one shallow minimum, but two equally high maxima within one magnetron period. If the offset is in the direction of one of the detection electrodes the PCD curve shows one high and one low maximum but two equally deep minima within one magnetron period. If the offset is directed between the excitation and detection electrodes, then “mixtures” of the above described cases appear. When the center of the offset magnetron orbit is moved back to the geometric axis of the ICR cell, the intensity oscillation of the satellite peak 2vR+vM becomes quite regular with two equally deep minima and two equally high maxima.
In an FT-ICR measurement, it is basically advantageous if the magnetron orbit has a relatively small diameter or if it does not exist at all. Unfortunately, experimental methods to reduce the magnetron motion with cooling using a resonant buffer gas are not generally applicable since they are very mass selective and require the introduction of relatively high amounts of gas into the ultrahigh vacuum chamber. In addition, it is also desirable that the axis of the magnetron orbit be as close as possible to the axis of the ICR cell. In the best case, it should be coaxial with the cell axis. A compromise would be a small magnetron orbit very close to the cell axis. If the electric field in the cell is asymmetric, its axis may be radially displaced against the cell axis. In this case, the magnetron orbit is also shifted and located around this radially displaced electric field axis.
For a good performance of any ICR cell the magnetron orbit size needs to be reduced, ideally minimized. If the electric field axis is radially displaced in reference to the cell axis, the magnetron orbit will also be displaced. It will be located around this radially displaced field axis, since the magnetron orbit winds around the electric field axis. Simulations of ion motion in the ICR cell show (as will be discussed in detail below) that, for example, the second harmonic peak with the frequency 2vR disappears if the magnetron orbit is concentric with the cell, i.e., if its center is on the cell axis. If the electric field axis does not coincide with the cell axis, i.e., if it is radially displaced, this will also shift the magnetron orbit radially to be wound around this offset electric field axis. Thus, the second harmonics peak will appear. On the other hand, the intensity of the satellite peak 2vR+vM of the second harmonic, for instance, increases with the radially offset position of the ion, both with the offset magnetron radius and/or offset magnetron orbit. In order to achieve small magnetron orbits which are as central as possible, electric field conditions are corrected or compensated for by using varying compensation voltages at least one, several or all individual mantle electrodes so that the intensities of, for example, the second harmonic and its satellite peak become as small as possible.
Most of the contemporary ion cyclotron resonance cells have a cylindrical geometry. In conventional ICR cells the excitation and detection electrodes are of equal size. They are four 90° segments of the cylinder mantle or, in other words, four individual electrodes covering an angular range of about 90°. For ion excitation, an oscillating electric field with several hundred volts amplitude can be used while the DC trapping voltages in a cell are in the range of 1-2 volts. Under these circumstances during the excitation process inhomogeneous oscillating fields are formed not only in the radial direction of the cell (transverse to the cell axis) but also in the longitudinal direction of the ICR cell.
If an ion is placed in an oscillating inhomogeneous electric field, it observes a force that drives it from a zone of higher electric field to a zone of lower electric field, i.e., from a zone with electric field lines of higher density to a zone with lower density of electric field lines. An effective electric potential can be defined to be responsible for this drift that is a function of the alternating electric field's amplitude and frequency, as well as the mass to charge ratio (m/z) of the affected ions. This potential is called the “pseudo potential” or the “effective potential”. Operation of RF multipole ion guides and Paul traps is based on this effect.
FIG. 14a schematically shows the direction of the movement of an ion in an inhomogeneous electric field due to the pseudo potential. An oscillating electric field between the curved electrodes 461, 462 of the two electrode system 460 is depicted in FIG. 14a. Electric field lines 463 of the alternating field are illustrated as double sided arrows, and the equipotential lines 464 are also shown. Due to the pseudo potential in the oscillating inhomogeneous electric field, ions tend to drift from higher field to lower field areas and orthogonal to the convex curvature of the equipotential lines 464. As a comparison, an oscillating homogenous field is shown in FIG. 14b between the parallel electrodes 471, 472 of the two electrode system 470 that is assumed to be of infinite extension to illustrate the effect. The oscillating homogeneous electric field has no such effect on the ions. Here the oscillating electric field is equally strong everywhere, the electric field lines 473 shown as double sided arrows here, and the equipotential lines 474 are parallel straight lines, and there are no special zones of the field ions would prefer, i.e., to which the ion in this oscillating field would drift. This indifference is shown with the double sided arrow 475 in a circle.
Similarly, the drift of the cyclotron orbit's center during a resonant cyclotron excitation is an effect due to the pseudo potential in the oscillating RF excitation field within the ICR cell. FIG. 15 shows a graph of the oscillating field equipotential lines 501 in a cross sectional view of a conventional cylindrical ICR cell 500. The cell mantle is divided into four 90° individual electrodes. The excitation process is performed using two 90° excitation electrodes 502, 503 opposite to each other, and the remaining two 90° electrodes 504, 505 are used for detection. Also in this figure, circles in dashed lines with arrows are used to show the drift direction of the cyclotron orbit during a resonant cyclotron excitation process. In the middle of the cross sectional view of the cell, there is an area with parallel equipotential lines. In this area 506 no cyclotron orbit drift will be observed during the cyclotron excitation, as long as the excited cyclotron orbit stays within parallel equipotential lines. As expected, a simulation of the excitation of a central cyclotron orbit does not show a displacement during the excitation process. In the circles 509, 510 the cyclotron orbit will move away from the excitation electrodes towards the center of the cell during a cyclotron excitation (which is shown in the simulation in FIG. 5a). In the areas indicated with the circles 507, 508 the cyclotron orbit will drift towards the detection electrodes during a cyclotron excitation process (as also shown in the cyclotron excitation simulation in FIG. 5b). In the areas 511, 512, 513, 514 the drift of the cyclotron orbits will be perpendicular to the cell radius and follows the convex equipotential lines in these areas. The shape of the equipotential lines helps predict and understand the simulated displacement direction of the cyclotron orbits during the resonant excitation. In the dashed ellipses 517, 518 which are relatively close to the excitation electrodes there are small areas of parallel and straight equipotential lines. When ions are in these zones during their cyclotron excitation, then they will experience no drift of the cyclotron orbit, i.e., a magnetron orbit will not be excited. However, these are not realistic conditions to fulfill. The convex equipotential lines in the areas 515, 516 which are very close to the excitation electrodes let us predict a drift direction of the cyclotron orbit towards (and not away from) the excitation plates. However these are zones which are too close to the electrodes and have no practical importance during (most of the) regular operations of an ICR cell.
FIG. 6 shows a PCD diagram 250 in which the change of the relative intensity of the peak with the measured frequency 2vR+vM is plotted as a function of the post capture delay time of the ions in the cell. As described above the PCD curve 251 shows maxima 260, 262, 264 and minima 261, 263. The distance between a first maximum 260 and a third maximum 262 corresponds to the period 252 of the magnetron motion, which is in this case about 200 ms. This in turn corresponds to a magnetron frequency of about 5 Hz. In the lower half of the figure the corresponding positions of an ion in the cell are shown, at which the cyclotron excitation took place. Here, the excitation electrodes 160, 161 and the detection electrodes 162, 163 can be seen in the cross sectional views of ICR cells. In these simulated pictures, ions start the cyclotron excitation at an ion position which is not on the cell axis. Starting positions of the ion cyclotron excitations are marked as white dots 270, 280 and the shift direction of the center of the cyclotron orbit during the excitation process is shown by white arrows 271, 281. As described above, this shift is in the direction 281 to a detection electrode 162 if the excitation process takes place near a detection electrode 162. This in turn means an excitation of the magnetron motion during the cyclotron excitation. However, if a cyclotron excitation is in the quadrant of an excitation electrode 160, the center of the cyclotron path is shifted away from the excitation electrode 160, in the direction 271 to the cell center. This in turn means a de-excitation or a relaxation of the magnetron motion during the cyclotron excitation.
If the axis of the DC field coincides with the ICR cell axis the cyclotron motion winds as a magnetron orbit on a circle around the cell axis. In this case, the maxima in the PCD curve should be equally high. However, in FIG. 6 the maxima in the PCD curve 251 are not equally high. They are alternatingly higher and lower. This means that the magnetron motion does not circle around the cell axis since the electric field axis is shifted.
An ideal dipole field for the cyclotron resonance excitation of ions is provided if the RF irradiation is performed using two infinitely large parallel planar electrodes. The excitation using a small planar electrode with a finite size together with the trapping electrodes perpendicular to it generates an inhomogeneous oscillating electric field. As shown above, an excitation using 90° electrodes of the cylindrical mantle also generates oscillating electric fields of which the really homogeneous range is only in a very small volume close to the axis of the cell, even if the electrodes would be infinitely large. As the ion gets excited to larger cyclotron orbits, it becomes exposed to rather inhomogeneous parts of the RF excitation field.
The largest homogeneous portion of the oscillating electric excitation field with parallel equipotential lines is obtained if 120° electrodes are used for ion excitation. This is described by Alan Marshall Group (61st ASMS Conference on Mass Spectrometry and Allied Topics, Jun. 9-13, 2013, Minneapolis, Minn.). Two 120° cylinder electrodes for excitation geometrically leave only space for two 60° detection electrodes within a circular cross section. However, it is not advantageous to detect with small electrodes like 60° since the generated image current signal will be smaller than a signal detected e.g., using 90° electrodes. Also the abundance of harmonics, especially second and third harmonic peaks is higher, as illustrated in FIGS. 18a-f and described below. The best solution would be also to detect with electrodes or electrically coupled electrode groups that each cover an angular range of 120°. In a cell having 2×120°/2×60° individual integral electrodes, these have to be inevitably the same electrodes which are also used for excitation. Electronically, it is possible to use one electrode for excitation and detection by switching an electrode from excitation to detection mode. Another possibility is using anti-parallel diodes to permanently connect the electrodes used for excitation and detection as described in conference presentations of Alan G. Marshall and coworkers [(1) Chen, T.; Kaiser, N. K.; Beu, S. C.; Hendrickson, C. L.; and Marshall, A. G., “Excitation and Detection with the Same Electrodes for Improved FT-ICR MS Performance”, 60th Proceedings of Annual Conference of American Society for Mass Spectrometry, Vancouver, BC, Canada, May 20-24, 2012, and (2) Chen, T.; Kaiser, N. K.; Beu, S. C.; Blakney, G. T.; Quinn, J. P.; Hendrickson, C. L.; and Marshall, A. G., “Improving Radial and Axial Uniformity of the Excitation Electric Field in a Closed Dynamically Harmonized FT-ICR Cell”, 61st Proceedings of Annual Conference of American Society for Mass Spectrometry, Minneapolis, Minn., USA, Jun. 9-13, 2013].
Using 120° excitation electrodes, the oscillating electric field in a quite large central region around the cell axis is homogeneous. As long as the ions remain in this zone a very good dipole excitation field is produced and virtually no drift of the cyclotron orbit is induced during the excitation process. In other words, the oscillating electric field used for cyclotron excitation does not excite or relax the ion's magnetron motion during the cyclotron excitation. If the ion is on an initial magnetron orbit prior to cyclotron excitation, the magnetron orbit retains its size during the cyclotron excitation.
The cross sectional view of an ICR cell 520 in FIG. 16a shows the equipotential lines 521 of the oscillating electric field applied to the 120° electrodes 522, 523 for the cyclotron excitation of ions. The remaining electrodes 524, 525 are 60° electrodes each. The equipotential lines in the relatively large area around the cell center are basically parallel straight lines. This part of the field looks similar to a field between two plane-parallel electrodes, as shown in FIG. 14b. In this zone, no drift of the cyclotron orbit during the resonant excitation process occurs. In the four other marked zones 527, 528, 529, 530, the drift during a cyclotron excitation is outward from the center. Cyclotron orbits are shifted in direction of the excitation or detection electrodes. In the areas between these circles, drifts perpendicular to the cell radius are expected.
In the central zone 526 with straight and parallel equipotential lines, since there is no remarkable drift of the cyclotron orbit during resonant excitation, there is also no excitation or relaxation of the magnetron motion, i.e., the magnetron orbit does not become larger or smaller after the cyclotron excitation of the ion. An oscillating post capture delay curve of the satellite peak of the second harmonic, as described in the afore-mentioned U.S. patent application Ser. No. 13/767,595, cannot be acquired if the ions are in this zone. In the zones outside this area, it is not too much different: close to the excite electrodes as well as detect electrodes, cyclotron orbits will be shifted towards those electrodes during a resonant excitation process, which also does not produce the oscillating PCD curve as known from the 90° excitation system.
In contrast, FIG. 16b shows a cross sectional view at a cylindrical cell 540 with two 120° 544, 545 and two 60° 542, 543 individual electrodes, where the excitation field in this case is generated between the two 60° individual electrodes. The equipotential lines 541 show a very inhomogeneous oscillating excitation field. A somewhat homogenous area is in the very middle of the cell in the dashed circle 546 in which the resonant cyclotron excitation would not induce a shift of the cyclotron orbit center, i.e., a change of the magnetron orbit size. This is indicated with the double sided arrow in the circle 546. There are two further small zones of nearly homogeneous field close to the 60° excitation plates 557, 558, which are not too relevant in this case. Operating in these zones would mean that the ion has a severely offset cyclotron motion, possibly as a result of an extremely large magnetron orbit around the cell axis or as a result of a smaller but severely offset magnetron orbit. In the even less relevant zones 555, 556 extremely close to the 60° excitation plates, the convexity of the equipotential lines shows that a cyclotron excitation in these zones would experience a center shift towards these excitation electrodes, but any cyclotron excitation of usable extent would cause ejection of any ion in this zone to the excitation electrodes. In the dashed ellipses 547, 548 in the quadrants of the 120° electrodes the resonant excitation of the ion cyclotron motion causes an orbit shift towards the 120° electrodes as shown with the arrows, which means an excitation of their magnetron orbit. In the dashed circles 549, 550 in the quadrants of the upper and lower 60° excitation plates the resonant excitation of the ion cyclotron motion causes an orbit shift towards the center of the cell, away from the excitation electrodes as shown with arrows, which means a relaxation (de-excitation) of their magnetron orbit. The arrows in the remaining dashed circles 551, 552, 553, 554 show the shift direction of the cyclotron orbit during a resonant excitation in each of these zones.
FIG. 17a shows a plot 560 demonstrating the effect of the cyclotron excitation on the magnetron orbit when the ion starts in the region of the excitation electrodes. The initial magnetron orbit diameter of the ion is 10% of the cell diameter. Curve 561 is obtained when an excitation using the 60° electrodes is simulated. It clearly shows the reduction of the magnetron orbit diameter. The curve 562 is obtained if an excitation using 90° electrodes is simulated. In this case the reduction of the magnetron orbit diameter is not as strong as in the case with excitation using the 60° electrodes. As the curves 562, 563 show, the reduction of the magnetron diameter at all excitation powers is stronger when excited with 60° electrodes, weaker when excited with 90° electrodes. The simulation of a cyclotron excitation using 120° electrodes is shown in curve 563. In this particular case the simulated curve shows practically no change of the magnetron radius. Simulations show, that depending on the initial phase of the ions and the initial phase of the exciting RF field the use of the 120° electrodes leads to no change or quite insignificant changes of the magnetron orbit.
FIG. 17b shows a plot 565 demonstrating the effect of the cyclotron excitation on the magnetron radius when the ion starts in the region of the detection electrodes. The initial magnetron orbit diameter of the ion is again 10% of the cell diameter. The curve 566 is obtained simulating an excitation using the 60° electrodes. This curve shows a significant increase of the magnetron orbit diameter. The curve 567 is obtained simulating an excitation using 90° electrodes. In this case the increase of the magnetron orbit diameter is not as strong as with the excitation using the 60° electrodes. As the curves 566, 567 show, the increase of the magnetron diameters at all excitation powers is stronger when excited with 60° electrodes, weaker when excited with 90° electrodes. The simulation of a cyclotron excitation using 120° electrodes is shown in curve 568. In this case the simulated curve shows an insignificant decrease of the magnetron radius.
In FIG. 17c the effect of the magnetron orbit center shift during the cyclotron excitation event is illustrated as simulated PCD curves for the excitation with 60° electrodes 571, 90° electrodes 572 and 120° electrodes 573. In all cases an initial magnetron orbit radius of 10% of the ICR cell radius on axis and the same final cyclotron excitation radius of 66% of the ICR cell radius is used for the simulations. The maxima 575, 576 directly correspond to one point on the curves 566, 567, 568 in FIG. 17b, the minima 577, 578 correspond to one point on the curves 561, 562, 563 in FIG. 17a. The distance 574 between two maxima 575, 576 is related to the magnetron frequency. The cyclotron excitation start phase (x-axis) is directly related to the post capture delay time in the measured PCD curve diagrams.
To have an ideal dipole excitation field in a relatively large zone at the center of the cell, as it is realized in the case of the 120° excitation electrodes, does not change the fact that the center of the radial DC field in the cell can be offset due to various reasons. The reasons can be chemical contamination and surface charging, mechanical misalignment, etc., as outlined above. A slightly offset radial DC field may be considered as negligible in the “picture” of the oscillating RF field, since the RF amplitude values are in the range of hundreds of volts, very high compared to the low DC voltages of the cell electrodes. In the absence of the oscillating electric field, when the cell acts as a trap only, even a slight offset, such as by 50 mV, can already be inacceptable and it can radially displace the magnetron motion by a significant amount.
In order to achieve a sensitive detection in an ICR cell with 120° excitation electrodes, the same 120° electrodes can be used for detection of the ions too, which is, although rarely used, a well-known technique. In addition, when detected with 120° electrodes the second and third harmonics are significantly suppressed and do not show up in the frequency or mass spectrum.
FIGS. 18a-f show a series of simulated spectra detected using 60°, 90°, and 120° electrodes of an FT-ICR cell. In these simulated spectra the frequency vM of the magnetron motion is chosen to be 10 frequency units (f.u., arbitrary), the reduced cyclotron frequency vR 100 frequency units (f.u., arbitrary) in order to achieve a better visualization. In reality the ratio of the cyclotron-to-magnetron frequency would be at least 1000. The leftmost peak 810 in the simulated spectra is the magnetron frequency vM and the second peak 820 is the reduced cyclotron frequency vR.
FIG. 18a depicts the simulated spectrum detected with 90° mantle electrodes as in a classical FT-ICR cell. The excited cyclotron radius is at 75% of the FT-ICR cell radius, the on-axis magnetron motion (around the cell axis) has a radius that is 16% of the cell radius. Due to the on-axis magnetron motion, as a result of averaging, the second harmonic 2vR 830 at 200 f.u. does not appear. Similarly, the fourth harmonic 4vR peak 850 itself is also not visible in this spectrum, neither is the sixth harmonic 6vR 870. Although all even harmonics do not appear in this spectrum due to the central magnetron orbit, the odd harmonics like 3vR 840 at 300 f.u. and 5vR 860 at 500 f.u. do appear.
The first sideband of the main cyclotron peak 820 is not visible in this spectrum but the second sideband 822 with the frequency of vR+2vM is there. Although the second harmonics is not visible its first satellite peak with the frequency of 2vR+vM 831 does appear at 201 f.u. with some significant abundance. A trace of a further satellite peak at 2vR+3vM 833 is also visible. Also visible are the first satellite peaks 851, 871 of the not appearing fourth and sixth harmonics 850, 870, respectively. Traces of the third satellite peaks 853, 873 are visible in both cases. Also second satellite peaks of the odd harmonics like 3vR and 5vR appear with very low abundances.
FIG. 18b depicts the simulated spectrum detected again with 90° mantle electrodes as in a classical FT-ICR cell. The excited cyclotron radius is at 66% of the FT-ICR cell radius, the magnetron motion has a radius that is 16% of the cell radius and is off axis by 8% of the cell radius. Due to the off-axis magnetron motion the second harmonics 2vR 830, as well as the fourth and the sixth harmonics 4vR 850 and 6vR 870 appear. The odd harmonics like 3vR 840 and 5vR 860 do also appear in the spectrum. The first sideband 821 of the main peak which was missing in the spectrum in FIG. 18a, as well as sidebands and satellite peaks off all harmonics are visible. An off axis magnetron orbit makes all harmonic peaks and their sidebands appear when detected with 90° mantle electrodes.
FIG. 18c depicts the simulated spectrum detected with 60° mantle electrodes. The excited cyclotron radius is at 75% of the FT-ICR cell radius, the on-axis magnetron motion (around the cell axis) has a radius that is 16% of the cell radius. Due to the on-axis magnetron motion, as a result of averaging, the second harmonic 2vR 830 at 200 fu. does not appear here in contrast to FIG. 18a. Similarly, the fourth harmonic 4vR peak 850 is also not visible in this spectrum, neither is the sixth harmonic 6vR 870. The third harmonic with the frequency 3vR 840 appears with a relatively high abundance and the fifth one with the frequency 5vR 860 also appears.
The first sideband of the main cyclotron peak 820 is here also not visible in this spectrum but the second sideband 822 with the frequency of vR+2vM is there. The first satellite peak 2vR+vM 831 of (not appearing) second harmonic appears with considerable abundance. A trace of a further satellite peak at 2vR+3vM 833 is also visible, while the first satellite peaks 851, 871 of the not appearing fourth and sixth harmonics 850, 870, respectively, are small. Traces of the third satellite peaks 853, 873 are visible in both cases. Also second satellite peaks of the odd harmonics like 3vR and 5vR appear with very low abundances.
FIG. 18d depicts the simulated spectrum detected again with 60° mantle electrodes in an FT-ICR cell. The excited cyclotron radius is here at 66% of the FT-ICR cell radius, the magnetron motion has a radius that is 16% of the cell radius and is off axis by 8% of the cell radius. Due to the off-axis magnetron motion all even harmonics like 2vR 830, 4vR 850 and 6vR 870 appear in the spectrum. Also the odd harmonics 3vR 840 and 5vR 860 also appear in the spectrum. The first sideband 821 of the main peak which was missing in the spectrum in FIG. 18a, as well as sidebands and satellite peaks off all harmonics are visible. Using 60° mantle electrodes for detection, an off axis magnetron orbit makes all harmonic peaks and their sidebands appear with much larger relative abundances compared to the 90° mantle electrodes detection.
FIG. 18e depicts the simulated spectrum detected with 120° mantle electrodes in an FT-ICR cell. The excited cyclotron radius is at 75% of the FT-ICR cell radius, the on-axis magnetron motion (around the cell axis) has a radius that is 16% of the cell radius. Due to the on-axis magnetron motion, as a result of averaging, even harmonics like the second harmonic 2vR 830, fourth harmonic 4vR 850 and sixth harmonic 6vR 870 do not appear. Odd harmonics like 3vR 840 and 5vR 860 do appear but they are extremely small. The sidebands 821, 822 of the main peak are not visible. Also the sidebands 831, 832 of the second harmonic 830 are vanishingly small. Visible are the second sideband (satellite) 3vR+2vM 842 of the third harmonic 3vR 840, first satellite 4vR+vM 851 of the fourth harmonic 4vR 850, the fifth harmonic itself 5vR 860 and its second satellite peak 5vR+2vM 862, and first satellite peak 6vR+vM 871 of the sixth harmonic 6vR.
FIG. 18f depicts the simulated spectrum detected again with 120° mantle electrodes in an FT-ICR cell. The excited cyclotron radius is here at 66% of the FT-ICR cell radius, the magnetron motion has a radius that is 16% of the cell radius and is off axis by 8% of the cell radius. Despite the off-axis magnetron motion the even harmonic 2vR 830 does not appear in the spectrum. Harmonics 4vR 850 and 6vR 870 are very small. Also the odd harmonic 3vR 840 does not appear. Harmonics 5vR 860 does appear but is very small. The sidebands 821, 822 of the main peak do not appear even here with the off-axis magnetron orbit. As a final remark, when detecting with 120° electrodes, even an off axis magnetron orbit cannot make all harmonic peaks and their sidebands appear, and if so, the abundance of these peaks is very low.
Table 1 in FIG. 19 focuses on the second harmonic peak and its most abundant (first) satellite when electrodes covering different angular ranges are used for excitation and detection. The entries in italics show cases which are not possible if specially divided cells with electrode mode (excitation/detection) switching are not used. As known from the simulated data displayed in FIGS. 18a-f the second harmonic peak does not appear in the spectrum if there is no magnetron orbit or if the magnetron orbit is around the cell axis. Additionally, when detected with 120° electrodes, neither the second harmonics nor their satellite peaks appear in the spectrum, regardless, which electrodes are used for excitation. Thus, the complete first row of the Table 1 shows no second harmonics and no first satellite peak. When excited using 90° electrodes, the detection with 90° electrodes does not result in a second harmonic peak if the magnetron orbit is around the cell axis. If the magnetron orbit is off axis, the second harmonic appears, but its intensity does neither vary nor oscillate with post capture delay time. If ions at an axial position or on an axial magnetron orbit are excited using 120° electrodes (or electrode groups) and detected with 60° electrodes (or electrode groups), still no second harmonics appear. A satellite peak of the second harmonics appears but it does not vary or oscillate with post capture delay time. If the ions are off axis the second harmonic peak and its satellite appears, but neither one of them does vary or oscillate with changing post capture delay time.
If ions at an axial position or on an axial magnetron orbit are excited using 60° electrodes and detected also with 60° electrodes, no second harmonic peak appears but the well-known satellite peak 2vR+vM appears and it oscillates with post capture delay time. In case of the off axis ions with the magnetron orbit off axis, the second harmonics and its satellite peak appear in the spectrum and the satellite peak oscillates with changing post capture delay time.
A 90° excitation possibility combined with 120° detection, 120° excitation and 90° detection, 60° excitation and 90° detection, as well as 90° excitation and 60° detection are also shown in the table. But they are special cases as they require a more complex division of the cell mantle electrodes or excitation/detection mode switching for the cell being capable of performing such particular applications.
As described above, the use of 120° excitation electrodes generates a homogeneous dipolar excitation field but it makes detection and correction of an offset electric DC field in the cell difficult. No drift of a radially offset cyclotron orbit will happen. Therefore, an electric field correction by observing and minimizing the harmonics will be difficult when using 120° electrodes for excitation and detection.
Due to the size of the electrodes, the detection with 60° electrodes (or electrode groups) leads to less abundant signals than the detection with 90° or 120° electrodes (or electrode groups). On the other hand, when detecting with 120° electrodes, a possible field axis displacement may not be detected since the even harmonics do not appear and remain here uncorrected. Therefore, a moderately sized, offset magnetron orbit cannot be corrected. A consequence of exciting and detecting with 120° segment electrodes is that the correction of a possible offset of the radial DC electric field in the ICR cell using the method according to the U.S. pending patent application Ser. No. 13/767,595 will not work.